Let us borrow some notation from [1]}. We embark with a complex connected simple algebraic group \(G(\mathbb {C})\)  which has finite center. Let \(\sigma \)  be a real form of \(G(\mathbb {C})\)  so that \(G=G(\mathbb {C})^{\sigma }\) . That is, \(\sigma \)  is an involutive antiholomorphic Lie group automorphism of \(G(\mathbb {C})\) . Let \(\theta \)  be the involutive algebraic automorphism of \(G(\mathbb {C})\)  corresponding to \(\sigma \)  via the Cartan theorem (see Theorem 3.2 of [1]}). Denote by \(K(\mathbb {C}):=G(\mathbb {C})^{\theta }\) .
